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Legendrian knots and exact Lagrangian cobordisms
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Algebra and Geometry. Inst Mittag Leffler, Aurav 17, S-18260 Djursholm, Sweden. (Geometri)
Univ So Calif, Los Angeles, CA 90089 USA.
Tokyo Inst Technol, Meguro Ku, Tokyo 1528551, Japan.
2016 (English)In: Journal of the European Mathematical Society (Print), ISSN 1435-9855, E-ISSN 1435-9863, Vol. 18, no 11, 2627-2689 p.Article in journal (Refereed) Published
Abstract [en]

We introduce constructions of exact Lagrangian cobordisms with cylindrical Legendrian ends and study their invariants which arise from Symplectic Field Theory. A pair (X, L) consisting of an exact symplectic manifold X and an exact Lagrangian cobordism L subset of X which agrees with cylinders over Legendrian links Lambda(+) and Lambda (-) at the positive and negative ends induces a differential graded algebra (DGA) map from the Legendrian contact homology DGA of Lambda(+) to that of Lambda (-) .We give a gradient flow tree description of the DGA maps for certain pairs (X, L), which in turn yields a purely combinatorial description of the cobordism map for elementary cobordisms, i.e., cobordisms that correspond to certain local modifications of Legendrian knots. As an application, we find exact Lagrangian surfaces that fill a fixed Legendrian link and are not isotopic through exact Lagrangian surfaces.

Place, publisher, year, edition, pages
2016. Vol. 18, no 11, 2627-2689 p.
National Category
Geometry
Identifiers
URN: urn:nbn:se:uu:diva-287988DOI: 10.4171/JEMS/650ISI: 000386876900007OAI: oai:DiVA.org:uu-287988DiVA: diva2:923681
Funder
Knut and Alice Wallenberg Foundation
Available from: 2016-04-27 Created: 2016-04-27 Last updated: 2016-12-01Bibliographically approved

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